The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Substitute Numbers for Letters in Calculations With Brackets

In this worksheet, students will replace letters with numbers and carry out questions using the four number operations, with some calculations in sets of brackets. They must give their final answers as numbers not letters.

Which of the calculations below shows the correct way to convert the letters into numbers?

10 + (7 x 4)

10 + (6 x 4)

10 x (7 x 4)

If a = 72, b = 9, c = 6 and d = 8, what is b + (a ÷d)?

Remember that when we have brackets in a question we solve the equation inside them first.

Can you finda ÷d first?

9

8

11

12

And now the final step to solve the problem:

If a = 72, b = 9, c = 6 and d = 8, what is b + (a ÷ d)?

We know from the last question that (a ÷ d) = 72÷ 8 = 9.

Now complete the rest of the equation and write your answer as a number.

TRUE or FALSE?

When I see numbers inside a bracket, I should always multiply them.

True

False

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

Which of the calculations below shows the correct way to convert the letters into numbers?

3 + (27 - 9)

3 + (27 x 9)

3 + (27 ÷ 9)

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

What part of the equation should be answered first?

3 + 27

27 ÷ 9

3 + 9

Let's put all the steps together now:

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

Work out the answer to the full equation and record your answer as a number.

Following on from the last question:

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

Which number are you adding A to?

3

18

4

36

Now you are going to be the examiner!

Three different students have been given the question below:

If a = 10, b = 40, c = 8 and d = 3, what is a + (b ÷ c)?

Which students have answered the question correctly by creating the right calculation from the information given?

Following on from the last question, we will now find the final answer as a number:

If a = 10, b = 40, c = 8 and d = 3, what is a + (b ÷ c)?

ANSWERS

Question 1

If A = 7, B = 10, C = 6 and D = 4, what is B (A x D)?

Which of the calculations below shows the correct way to convert the letters into numbers?

CORRECT ANSWER

10 x (7 x 4)

EDDIE SAYS

The question tells us that B = 10, A = 7 and D = 4.
If we swap these numbers in for the letters, then B (A x D) becomes 10 (7 x 4).
It may look like a mistake has been made in the question, as there is no symbol between the letter B and the brackets. When this happens it means you should multiply the contents of the bracket by the number that comes before it. Or, in other words, you need to assume that a multiplication has been missed out.
So 10 (7 x 4) is the same as 10 x (7 x 4).

ANSWERS

Question 2

If a = 72, b = 9, c = 6 and d = 8, what is b + (a ÷d)?

Remember that when we have brackets in a question we solve the equation inside them first.

Can you finda ÷d first?

CORRECT ANSWER

9

EDDIE SAYS

The question tells us that a = 72 and d = 8.
When we divide 72 by 8, we reach the answer of 9.
The first step to solving the problem is now complete! Let's move on to the next step...

ANSWERS

Question 3

And now the final step to solve the problem:

If a = 72, b = 9, c = 6 and d = 8, what is b + (a ÷ d)?

We know from the last question that (a ÷ d) = 72÷ 8 = 9.

Now complete the rest of the equation and write your answer as a number.

CORRECT ANSWER

18

EDDIE SAYS

The question tells us that b = 9.
If we swap this number in for the letter in the rest of the equation, then b + (9) becomes 9 + 9.
When we add 9 and 9, we reach the answer of 18.
Were you able to complete the final step to reach the correct answer? Let's try another for some more practise...

ANSWERS

Question 4

TRUE or FALSE?

When I see numbers inside a bracket, I should always multiply them.

CORRECT ANSWER

False

EDDIE SAYS

This statement is FALSE.
The brackets show us the part of the sum that needs to be worked out first; this may be a multiplication sum but it could equally be addition, subtraction and/or division.

ANSWERS

Question 5

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

Which of the calculations below shows the correct way to convert the letters into numbers?

CORRECT ANSWER

3 + (27 ÷ 9)

EDDIE SAYS

The question tells us that A = 3, B = 27 and C = 9.
If we swap these numbers in for the letters, then A + (B ÷ C) becomes 3 + (27 ÷ 9).
The brackets are very important - can you remember why?

ANSWERS

Question 6

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

What part of the equation should be answered first?

CORRECT ANSWER

27 ÷ 9

EDDIE SAYS

The brackets tell us which part of the calculation to work out first.
So we should calculate the sum in brackets first which is B ÷ C.
The question tells us that B = 27 and C = 9.
If we swap these numbers in for the letters, then B ÷ C becomes 27 ÷ 9.

ANSWERS

Question 7

Let's put all the steps together now:

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

Work out the answer to the full equation and record your answer as a number.

CORRECT ANSWER

6

EDDIE SAYS

We already know that we must calculate the bracket first, which gives us an answer of 3.
The question tells us that A = 3. If we swap that into the rest of the equation then A + (3) becomes 3 + 3.
When you add 3 and 3, we reach an answer of 6.
Great work putting all those steps together maths coder!

ANSWERS

Question 8

Following on from the last question:

If A = 3, B = 27, C = 9 and D = 2, what is A + (B ÷ C)?

Which number are you adding A to?

CORRECT ANSWER

3

EDDIE SAYS

In the last question, we worked out that (B ÷ C) needs to be worked out first.
We substituted the letters for numbers to get the sum 27 ÷ 9.
If we divide 27 by 9, we reach the answer of 3.
This needs to be added to A to reach the correct answer.

ANSWERS

Question 9

Now you are going to be the examiner!

Three different students have been given the question below:

If a = 10, b = 40, c = 8 and d = 3, what is a + (b ÷ c)?

Which students have answered the question correctly by creating the right calculation from the information given?

CORRECT ANSWER

EDDIE SAYS

The question tells us that a = 10, b = 40 and c = 8.
If we swap these numbers in for the letters then a + (b ÷ c) becomes 10 + (40 ÷ 8).
We need to complete the calculation in brackets first, so the order we need to work in is 40 ÷ 8 + 10.
So only the second student would reach the right answer!
How did you find being the examiner? Was it easy or hard to spot the students' errors?

ANSWERS

Question 10

Following on from the last question, we will now find the final answer as a number:

If a = 10, b = 40, c = 8 and d = 3, what is a + (b ÷ c)?

CORRECT ANSWER

15

EDDIE SAYS

The question tells us that a = 10, b = 40 and c = 8.
If we swap these numbers in for the letters, then a + (b ÷ c) becomes 10 + (40 ÷ 8).
We must work out the brackets first so 40 divided by 8 is 5.
Then we need to add 10 to this total, so we will reach an answer of 15.
Did you put the steps together in the right order to reach the correct answer?

Please provide your email address to download the guide

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.